Wouldn't the neutral solution be to pick a target standard of living (roughly approximated by something like a 75th percentile market rate salary, or whatever metric you chose) and pay that for any given location?

I'm aware of several teams that have done this with success in the past. Everybody, no matter their region of choice, gets compensation enough to enable an appropriately comfortable standard of living desired based on the actual costs of living where they choose. This is what we're talking about when we advocate for adjusting salaries for COL. It creates incentive for your employees to live where they actually want to live, work, and be happy - rather than wherever they feel like they can extract the most cash value from the company.